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Friction — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsFriction5 Marks
Question
The angle between the resultant contact force and the normal force exerted by a body on the other is called the angle of friction. Show that, if $\lambda$ be the angle of friction and la the coefficient of static friction, $\lambda\leq\tan^{-1}\mu.$
✓

Answer



$f \rightarrow $ applied force
$F_i \rightarrow $ contact force
$F \rightarrow $ frictional force
$R \rightarrow $ normal reaction
$\mu=\tan\lambda=\frac{\text{F}}{\text{R}}$
When $\text{F}=\mu\text{R, F}$ is the limiting friction $($max friction$)$. When applied force increase, force of friction increase upto limiting friction $(\mu\text{R})$
Before reaching limiting friction

$\text{F}<\mu\text{R}$
$\therefore\tan\lambda=\frac{\text{F}}{\text{R}}\leq\frac{\mu\text{R}}{\text{R}}\Rightarrow\tan\lambda\leq\mu\Rightarrow\lambda\leq\tan^{-1}\mu$

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